Skip to main content
SpringerLink
Log in

Design of band-gap grid structures

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

This paper discusses issues related to designing band-gaps in periodic plane grid structures. Finite element analysis is used to solve the dynamic behavior of a representative unit cell and Bloch–Floquet theory is used to extend the results to the infinite structure. Particular attention is given to the addition of non-structural masses that are introduced as design variables. These are used to create desirable features in the dispersion diagram. Physical insight is presented into the optimal choice of locations where masses should be added and the results of several numerical examples are provided to highlight this and other features of how band-gaps can be created and located at desired frequency ranges. The effect of the skew angle of the underlying grid structure is also explored, as are mathematical refinements of the modelling of the beam elements and the rotational inertia of the added masses. A scaling feature between the size of the reducible and the irreducible reference cell is exploited and the manner in which this can simplify optimization approaches is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Brillouin Brillouin L (1953) Wave propagation in periodic structures. 2nd edn. New York: Dover

  2. Cox00 Cox SJ, Dobson DC (2000) Band structure optimization of two-dimensional photonic crystals in H-polarization, J Comput Phys 158:214–224

  3. Cox99 Cox SJ, Dobson DC (1999) Maximizing band-gaps in two-dimensional photonic crystals. SIAM J Appl Math 59:2108–2120

  4. Diaz Diaz A, Benard A (2001) On the discretization of problems involving periodic planar tilings. Commun Numer Methods Eng 17:543–549

    Google Scholar 

  5. Dowling Dowling J, Everitt H (2004) Sonic band-gap bibliography, http://home.earthlink.net/∼jpdowling/pbgbib.html

  6. Heckel Heckel MA (1964) Investigations on the vibrations of grillages and other simple beam structures J Acoust Soc Am 36:1335–1343

    Google Scholar 

  7. Jensen Jensen JS (2003) Phononic band-gaps and vibrations in one-and two-dimensional mass-spring structures. J Sound Vib 266:1053–1078

    Google Scholar 

  8. Kafesaki Kafesaki M, Sigalas MM, Economou EN (1995) Elastic wave band-gaps in 3-D periodic polymer matrix composites. Solid State Commun 96(5):285–289

    Google Scholar 

  9. Langlet Langlet P, Hladky-Hennion A-C, Decarpigny JN (1995) Analysis of the propagation of plane acoustic waves in passive periodic materials using the finite element method. J Acoust Soc Am 98:2792–2800

    Google Scholar 

  10. Ma Ma L, Diaz A, Haddow A (2004) Modeling and design of materials for controlled wave propagation in plane grid structures. Paper DETC2004-57183, Proc. of DETC’04, ASME 2004 Design Engineering Technical Conf., Salt Lake City, UT

  11. Martinsson Martinsson PG, Movchan AB (2003) Vibrations of lattice structures and phononic band-gaps. Q J Mech Appl Math 56(1):45–64

    Google Scholar 

  12. Orris Orris RM, Petyt M (1974) A finite element study of harmonic wave propagation in periodic structures. J Sound Vib 33:223–236

    Google Scholar 

  13. Parmley Parmley S, Zobrist T, Clough T, Perez Miller A, Makela M, Yu R (1995) Phononic band structure in a mass chain. Appl Phys Lett 67(6):777–779

    Google Scholar 

  14. Sigalas Sigalas M, Economou E (1994) Elastic waves in plates with periodically placed inclusions. J Appl Phys 75(6):2845–2850

    Google Scholar 

  15. Sigmund Sigmund O (2001) Microstructural design of elastic band-gap structures. Proc. of the Second World Congress of Struct. and Multidisc. Optim., Dalian, China

  16. SigmundJensen Sigmund O, Jensen JS (2002) Topology optimization of phononic band-gap materials and structures. Fifth World Congress on Computational Mechanics, Vienna, Austria

  17. SigmundJensen03 Sigmund O, Jensen JS (2003) Systematic design of phononic band-gap materials and structures by topology optimization. Phil Trans R Soc Lon A 361:1001–1019

  18. Svanberg Svanberg K (1987) The method of moving asymptotes. Int J Numer Mech Eng 24:459–373

    Google Scholar 

  19. Vasseur Vasseur JO, Deymier PA, Frantziskonis G, Hong G, Djafari-Rouhani B, Dobrzynski L (1998) Experimental evidence for the existence of absolute acoustic band-gaps in two-dimensional periodic composite media. J Phys Condens Matter 10:6051–6064

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Michigan State University, East Lansing, MI, 48824-1226, USA

    A.R. Diaz, A.G. Haddow & L. Ma

Authors
  1. A.R. Diaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A.G. Haddow
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A.R. Diaz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Diaz, A., Haddow, A. & Ma, L. Design of band-gap grid structures. Struct Multidisc Optim 29, 418–431 (2005). https://doi.org/10.1007/s00158-004-0497-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-004-0497-6

Keywords

Search

Navigation